In Schweser, sometimes bond duration is referred in terms of time (i.e. Macaulay’s duration, which is the time required to recoup your investment), and in other places, it is referred in the regular way i.e. (change in price/ change in yield). Can someone explain me the relationship between these two types of durations??
http://www.analystforum.com/phorums/read.php?13,926751,926982#msg-926982 I posted on this topic last year…
Thanks mwvt9, I read the last years discussion, but i still have some doubts. I am still unable to connect the pieces, especially the relationship between the two definitions of durations. So I have reopened last years discussion. Hoping to get some more views on duration and bell the concept once and for all…its been giving me sleepless nights;-)
Btw, last years discussion on duration was under the title “Understanding duration”
Think of it this way - Maccauleys - explains the math. Its the weighted average of cash flows. Good for explaining duration but no practical use. Modified - duration of choice for option free bonds. This mothod captures the fact that duration is “modified” as the price and yield change. Modified duration does not capture interest rate optionality so it cannot be used with MBS, callables etc Effective - Duration of choice for bonds with optionality. Also can be called OAS duration. This method uses a binomial tree to find bond prices in various interest rate scenarios and works backwards to an OAS and duration.
well said, 1morelevel
I am reading SS5 in Schweser and there is a mention of duration of liabilities with regards to asset/liability management . This may be a dumb question, but does this in any way relate to bond duration (interest rate sensitivity) or is this simply a measure of the time until your liabilities come due?
The duration has three definitions:
-
It is slope of Price-Yield curve at current market YTM
-
It is weighted average time in years - Macaulay Duration
-
It is %bond price change per 1% yield change with negative sign
If it is given in time say 6.76 years you can remove years and use just 6.76 for duration in (duaration= - % change in bond price/ % change in yield) formula
Macaulay and Modified duration are only good for option free bonds since they don,t take CF in account.
Effective Duration can be used for bonds with option. Best measure for interest rate risk. Take CF into account
No, it isn’t.
That slope gives you the price change of the bond for a 1% change in its yield, but not the percentage price change; (modified or effective) duration gives you the (negative of) the percentage price change.
Specifically, the present-value-of-cash-flow-weighted-average time to receipt of cash flows.
This is modified duration (assuming cash flows don’t change when YTM changes) or effective duration (if cash flows might change when YTM changes).
Note that the units for all types of duration are years.
More specifically, option-free _ fixed-coupon _ bonds.
They do take cash flows into account. What they don’t do is allow that those cash flows might change when YTM changes.
Also for floating-rate bonds.
And any other bonds.